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x^3-1

Integral of x^3-1 dx

Limits of integration:

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The graph:

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The solution

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02(x31)dx\int\limits_{0}^{2} \left(x^{3} - 1\right)\, dx
Integral(x^3 - 1, (x, 0, 2))
Detail solution
  1. Integrate term-by-term:

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n1n \neq -1:

      x3dx=x44\int x^{3}\, dx = \frac{x^{4}}{4}

    1. The integral of a constant is the constant times the variable of integration:

      (1)dx=x\int \left(-1\right)\, dx = - x

    The result is: x44x\frac{x^{4}}{4} - x

  2. Add the constant of integration:

    x44x+constant\frac{x^{4}}{4} - x+ \mathrm{constant}


The answer is:

x44x+constant\frac{x^{4}}{4} - x+ \mathrm{constant}

The answer (Indefinite) [src]
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(x31)dx=C+x44x\int \left(x^{3} - 1\right)\, dx = C + \frac{x^{4}}{4} - x
The graph
0.02.00.20.40.60.81.01.21.41.61.8-1010
The answer [src]
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Numerical answer [src]
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The graph
Integral of x^3-1 dx

    Use the examples entering the upper and lower limits of integration.